The finite elements (FEM) method is particularly useful when a robust
approximation is sought to solve partial differential equations on an
inhomogeneous mesh.
Solid mathematical foundations and a great deal of generality allow for
different implementations that are only sketched in the first section:
an example given for the advection-diffusion equation, for example,
shows how the Crank-Nicholson method described in the previous section
is only a particular case of a finite elements scheme.